Infinite number of perpendicular vectors?

AI Thread Summary
The discussion revolves around finding unit vectors that are orthogonal to given vectors A and B. After successfully determining unit vectors A' and B', the focus shifts to constructing all unit vectors C that are orthogonal to A' and B'. The question arises whether there are infinitely many vectors that satisfy the orthogonality condition with respect to C and another vector D. It is concluded that while there are indeed infinite vectors, the task only requires finding one specific vector D that meets the criteria.
Maybe_Memorie
Messages
346
Reaction score
0

Homework Statement


Let A and B be vectors
A = (2,-1,3) B = (1,4,1)
a) Find unit vectors A' and B' parallel to A and B respectively. Done.

b) Construct all the unit vectors C, orthogonal to A' and B'. Done.

c) Construct a unit vector, D, such that
C.D = 0.


Isn't there an infinite number of vectors that meet this criteria?
 
Physics news on Phys.org
Maybe_Memorie said:
b) Construct all the unit vectors C, orthogonal to A' and B'. Done.

c) Construct a unit vector, D, such that
C.D = 0.


Isn't there an infinite number of vectors that meet this criteria?

Well I think they just want you to find one, which you can do since you did part b already.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

To find the component of a vector perpendicular to another
Replies
20
Views
3K
Vectors: Proving the value of a•(b x c)
Replies
21
Views
8K
I Non orthogonal basis and the lines of its coordinate grid
Replies
9
Views
3K
Writing a vector parallel and normal to a unit vector ##\hat n##
Replies
26
Views
1K
I with this question about vectors
2
Replies
63
Views
6K
Vector dot product and parallel vectors
Replies
6
Views
4K
What is the relationship between vectors perpendicular to (1,1,1) and (1,2,3)?
Replies
5
Views
1K
Finding the Angle Between a Vector in the yz-Plane and Another Vector
Replies
11
Views
7K
Vector of shortest distance between two skew lines
Replies
11
Views
3K
Colinear points in a vectorplane
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top